Robert Svarc

Interpreting spacetimes of any dimension using geodesic deviation

We present a general method which can be used for geometrical and physical interpretation of an arbitrary spacetime in four or any higher number of dimensions. It is based on the systematic analysis of relative motion of free test particles. We demonstrate that local effect of the gravitational field on particles, as described by equation of geodesic deviation with respect to a natural orthonormal frame, can always be decomposed into a canonical set of transverse, longitudinal and Newton-Coulomb-type components, isotropic influence of a cosmological constant, and contributions arising from specific matter content of the universe. In particular, exact gravitational waves in Einsteins theory always exhibit themselves via purely transverse effects with D(D-3)/2 independent polarization states. To illustrate the utility of this approach we study the family of pp-wave spacetimes in higher dimensions and discuss specific measurable effects on a detector located in four spacetime dimensions. For example, the corresponding deformations caused by a generic higher-dimensional gravitational waves observed in such physical subspace, need not be tracefree.

The global existence, uniqueness and 1-regularity of geodesics in nonexpanding impulsive gravitational waves

We study geodesics in the complete family of nonexpanding impulsive gravitational waves propagating in spaces of constant curvature, that is Minkowski, de Sitter and anti-de Sitter universes. Employing the continuous form of the metric we prove existence and uniqueness of continuously dierentiable geodesics (in the sense of Filippov) and use a C 1 -matching procedure to explicitly derive their form.

The regularity of geodesics in impulsive pp-waves

We consider the geodesic equation in impulsive pp-wave space-times in Rosen form, where the metric is of Lipschitz regularity. We prove that the geodesics (in the sense of Carathéodory) are actually continuously differentiable, thereby rigorously justifying the

Refraction of geodesics by impulsive spherical gravitational waves in constant-curvature spacetimes with a cosmological constant

{\mathcal C}^1

Exact solutions to quadratic gravity

C1-matching procedure which has been used in the literature to explicitly derive the geodesics in space-times of this form.

Completeness of general pp-wave spacetimes and their impulsive limit

We investigate the fully general class of non-expanding, non-twisting and shear-free D-dimensional geometries using the invariant form of geodesic deviation equation which describes the relative motion of free test particles. We show that the local effect of such gravitational fields on the particles basically consists of isotropic motion caused by the cosmological constant Lambda, Newtonian-type tidal deformations typical for spacetimes of algebraic type D or II, longitudinal motion characteristic for spacetimes of type III, and type N purely transverse effects of exact gravitational waves with D(D-3)/2 polarizations. We explicitly discuss the canonical forms of the geodesic deviation motion in all algebraically special subtypes of the Kundt family for which the optically privileged direction is a multiple Weyl aligned null direction (WAND), namely D(a), D(b), D(c), D(d), III(a), III(b), IIIi, IIi, II(a), II(b), II(c) and II(d). We demonstrate that the key invariant quantities determining these algebraic types and subtypes also directly determine the specific local motion of test particles, and are thus measurable by gravitational detectors. As an example, we analyze an interesting class of type N or II gravitational waves which propagate on backgrounds of type O or D, including Minkowski, Bertotti-Robinson, Nariai and Plebanski-Hacyan universes.

Gyratonic pp-waves and their impulsive limit

We investigate motion of test particles in exact spacetimes with an expanding impulsive gravitational wave which propagates in a Minkowski, a de Sitter, or an anti-de Sitter universe. Using the continuous form of these metrics we derive explicit junction conditions and simple refraction formulas for null, timelike, and spacelike geodesics crossing a general impulse of this type. In particular, we present a detailed geometrical description of the motion of test particles in a special class of axially symmetric spacetimes in which the impulse is generated by a snapped cosmic string.

Algebraic structure of Robinson?Trautman and Kundt geometries in arbitrary dimension

We present the Riemann and Ricci tensors for a fully general non-twisting and shear-free geometry in arbitrary dimension D. This includes both the non-expanding Kundt and expanding Robinson-Trautman family of spacetimes. As an interesting application of these explicit expressions we then integrate the Einstein equations and prove a surprising fact that in any D the Robinson-Trautman class does not admit solutions representing gyratonic sources, i.e., matter field in the form of a null fluid (or particles propagating with the speed of light) with an additional internal spin. Contrary to the closely related Kundt class and pp-waves, the corresponding off-diagonal metric components thus do not encode the angular momentum of some gyraton. Instead, we demonstrate that in standard D=4 general relativity they directly determine two independent amplitudes of the Robinson-Trautman exact gravitational waves.